The mean credit card debt for a 30 year old FEMALE living in NYC is approximatel

Question

The mean credit card debt for a 30 year old FEMALE living in NYC is approximately normally distributed with a mean debt of $8,478 and a standard deviation of $1,665. For parts a thru c, what is the probability that a 30 year old FEMALE living in NYC selected at random will have:

a) Acreditcarddebtlessthan$6,000?

b) A credit card debt greater that $13,000?

c) Acreditcarddebtbetween$7,000and$10,000?

d) What minimum credit card debt that would separate the highest 5% credit card debt for a 30 year old female living in NYC?

Explanation / Answer

a) P(X < 6000)

= P(z < (6000 - 8478)/1665)

= P(z < -1.49)

= 0.0683

b) P(X > 13000)

= P(z > (13000 - 8478)/1665)

= P(z > 2.72)

= 0.0033

c) P(7000 < X < 10000)

= P(-0.89 < X < 0.91)

= 0.6323

d) For top 5%, z = 1.645

Hence,

Amount that separates top 5%

= 8478 + 1.645(1665)

= 11216.93

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